Problem: Simplify the following expression: $x = \dfrac{99p + 11}{66p - 88}$ You can assume $p \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $99p + 11 = (3\cdot3\cdot11 \cdot p) + (11)$ The denominator can be factored: $66p - 88 = (2\cdot3\cdot11 \cdot p) - (2\cdot2\cdot2\cdot11)$ The greatest common factor of all the terms is $11$ Factoring out $11$ gives us: $x = \dfrac{(11)(9p + 1)}{(11)(6p - 8)}$ Dividing both the numerator and denominator by $11$ gives: $x = \dfrac{9p + 1}{6p - 8}$